8.8.3.47 IfcTriangulatedFaceSet
8.8.3.47.1 Semantic definition
The IfcTriangulatedFaceSet is a tessellated face set with all faces being bound by triangles. The faces are constructed by implicit polylines defined by three Cartesian points. Depending on the value of the inherited attribute Closed the instance of IfcTriangulatedFaceSet represents:
 if TRUE, a boundary representation (or Brep);
 if FALSE, a face based surface representation.
The coordinates of each point are provided by a onebased index into an ordered list of Cartesian points provided by the twodimensional list CoordIndex, where
 the first dimension of the twodimensional list addresses the list of triangular faces;
 the second dimension of the twodimensional list provides exactly three indices. Each index points to a Cartesian point being a vertex of the triangle.
Depending on the provision of PnIndex the indices point either directly into the IfcCartesianPointList3D referenced by Coordinates defined at the supertype IfcTessellatedFaceSet, or they point into the PnIndex where the integer values at that position provides the location of the coordinate values within the IfcCartesianPointList3D. See Figure 8.8.3.47.A for the handling of point index.
See Figure 8.8.3.47.B for using the IfcTriangulatedFaceSet without (as default) and with using the PnIndex.
Optionally normals can be provided. Only normals per vector are supported allowing for visually curved triangles when the three normals of the corresponding three vertices of a triangle are not colinear to the normal of the triangular face. If they are identical, normals shall be omitted.
Normals are provided by the twodimensional list Normals, where
 the first dimension of the twodimensional list addresses the corresponding list of vertex indices of the triangular faces;
 the second dimension of the twodimensional list provides exactly three real values to determine the direction of the normal at this vertex of the triangle.
The indices in the CoordIndex point into the list of Normals. The indices of CoordIndex are applied to both points, either directly directly, or via the PnIndex and normals. See Figure 8.8.3.47.C for handling of normals.
Figure 8.8.3.47.D shows the use of IfcTriangulatedFaceSet without annotation. The diagram of the IfcTriangulatedFaceSet represents the indices and the ordered list into which the indices point. The index starts with 1 (indexed as 1 to N), if the greatest index in CoordIndex in N, then the IfcCartesianPointList shall have N lists of 3:3 coordinates.
Figure 8.8.3.47.D shows an IfcTriangulatedFaceSet represented by:
CoordIndex:
((1,6,5), (1,2,6), (6,2,7), (7,2,3), (7,8,6), (6,8,5), (5,8,1), (1,8,4), (4,2,1), (2,4,3), (4,8,7), (7,3,4))
IfcCartesianPointList3D:
((0.,0.,0.), (1.,0.,0.), (1.,1.,0.), (0.,1.,0.), (0.,0.,2.), (1.,0.,2.), (1.,1.,2.), (0.,1.,2.))
Informal Propositions
 If Closed = TRUE, the same topological constraints as imposed by an faceted boundary representation shall be safisfied. In particular:
 each face shall be unique;
 each edge shall be used by exactly two boundaries of faces;
 the topological normal at each point on the boundary of the triangulated face set shall point away from the material of the solid.
8.8.3.47.2 Entity inheritance

 IfcTessellatedItem
 IfcAnnotationFillArea
 IfcBooleanResult
 IfcBoundingBox
 IfcCartesianPointList
 IfcCartesianTransformationOperator
 IfcCsgPrimitive3D
 IfcCurve
 IfcDirection
 IfcFaceBasedSurfaceModel
 IfcFillAreaStyleHatching
 IfcFillAreaStyleTiles
 IfcGeometricSet
 IfcHalfSpaceSolid
 IfcLightSource
 IfcPlacement
 IfcPlanarExtent
 IfcPoint
 IfcSectionedSpine
 IfcSegment
 IfcShellBasedSurfaceModel
 IfcSolidModel
 IfcSurface
 IfcTextLiteral
 IfcVector
8.8.3.47.3 Attributes
#  Attribute  Type  Description 

IfcRepresentationItem (2)  
LayerAssignment  SET [0:1] OF IfcPresentationLayerAssignment FOR AssignedItems 
Assignment of the representation item to a single or multiple layer(s). The LayerAssignments can override a LayerAssignments of the IfcRepresentation it is used within the list of Items. 

StyledByItem  SET [0:1] OF IfcStyledItem FOR Item 
Reference to the IfcStyledItem that provides presentation information to the representation, e.g. a curve style, including colour and thickness to a geometric curve. 

IfcTessellatedFaceSet (4)  
1  Coordinates  IfcCartesianPointList3D 
An ordered list of Cartesian points used by the coordinate index defined at the subtypes of IfcTessellatedFaceSet. 
HasColours  SET [0:1] OF IfcIndexedColourMap FOR MappedTo 
Reference to the indexed colour map providing the corresponding colour RGB values to the faces of the subtypes of IfcTessellatedFaceSet. 

HasTextures  SET [0:?] OF IfcIndexedTextureMap FOR MappedTo 
Reference to the indexed texture map providing the corresponding texture coordinates to the vertices bounding the faces of the subtypes of IfcTessellatedFaceSet. 

*  Dim  IfcDimensionCount 
This attribute is formally derived.
The space dimensionality of this geometric representation item, it is always 3. 
Click to show 6 hidden inherited attributes Click to hide 6 inherited attributes  
IfcTriangulatedFaceSet (5)  
2  Normals  OPTIONAL LIST [1:?] OF LIST [3:3] OF IfcParameterValue 
An ordered list of three directions for normals. It is a twodimensional list of directions provided by three parameter values. * The first dimension corresponds to the vertex indices of the Coordindex * The second dimension has exactly three values, [1] the xdirection, [2] the ydirection and [3] the zdirections 
3  Closed  OPTIONAL IfcBoolean 
Indication whether the face set is a closed shell (TRUE) or an open shell (FALSE). If omitted no such information can be asserted. 
4  CoordIndex  LIST [1:?] OF LIST [3:3] OF IfcPositiveInteger 
Twodimensional list for the indexedbased triangles, where * The first dimension represents the triangles (from 1 to N) * The second dimension has exactly three values representing the indices to three vertex points (from 1 to 3). 
5  PnIndex  OPTIONAL LIST [1:?] OF IfcPositiveInteger 
The list of integers defining the locations in the IfcCartesianPointList3D to obtain the point coordinates for the indices withint the CoordIndex. If the PnIndex is not provided the indices point directly into the IfcCartesianPointList3D. 
*  NumberOfTriangles  IfcInteger 
This attribute is formally derived.
Derived number of triangles used for this triangulation. 
8.8.3.47.4 Examples
8.8.3.47.5 Formal representation
ENTITY IfcTriangulatedFaceSet
SUPERTYPE OF (ONEOF
(IfcTriangulatedIrregularNetwork))
SUBTYPE OF (IfcTessellatedFaceSet);
Normals : OPTIONAL LIST [1:?] OF LIST [3:3] OF IfcParameterValue;
Closed : OPTIONAL IfcBoolean;
CoordIndex : LIST [1:?] OF LIST [3:3] OF IfcPositiveInteger;
PnIndex : OPTIONAL LIST [1:?] OF IfcPositiveInteger;
DERIVE
NumberOfTriangles : IfcInteger := SIZEOF(CoordIndex);
END_ENTITY;